Electronic states in usual periodic structures are given by the periodicity like Bloch theorem. Introducing non-periodicity into the lattice, the electronic states with singular coherency of electron wavefunctions can be expected. We have focused on the periodic modulation (Fractal etc.) of lattice, and carried on the fablication and the characterization of periodic-modulated superlattices, as novel functional materials. The results of this study are summarized as follows.(1)Development of atomic-layer manipulation technologies for superlattice : (GaAs)m(GaP)n and (AIP)m(GaP)n atomic-layer superlattices have been successfully realized by atomic layer epitaxy(ALE), and also the inter-diffusion between the mono-layer lattice has been discussed.(2)Periodic modulation of superlattice with atomic-layer accuracy : GaAs/GaP and AlP/GaP periodic-modulated superlattices have been successfully realized with atomic-layer accuracy by the ALE technologies. Periodic, quasi-periodic (Fractal), random
… More, and multi-periodic structures have been used as the modulated structures, and especially Fibonacci progression has been used as Fractal structures.(3)X-ray analysis of the periodic-modulated superlattices : The XRD pattern of quasi-periodic superlattice shows no periodicity but self-similar geometry, and is consistent with the FFT spectrum of a Fractal structure. Also the X-ray reflection measurement of multi-periodic superlattice shows that the reflection wavelength can be controlled with sub-monolayer accuracy by modulation of the periodicity. This suggests the possibility of application to X-ray mirrors.(4)Optical characterization of electronic states in the periodic-modulated superlattices : Photo-reflectance spectrum of quasi-periodic, random superlattices show peculiar splitting of the subband (electronic states) in comparison with that of the periodic lattice, and are consistent with a transfer matrix calculation for the lattices. This result suggests that the control of electronic state can be possible artificially due to the periodic modulation using the ALE technologies.(5)Application to X-ray mirrors : We have discussed the application of periodic modulation for the lattice to X-ray mirror. Introducing the multiple period into atomic layer superlattice, the reflection wavelength can be controlled arbitrary with sub-monolayer accuracy that is needed to X-ray mirrors. Less